Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    18
    ReputationRep:
    1. Find the quadratic equation whose roots are (α + 1) and (β + 1), where α and β are the roots of the equation 2x2 - 11x + 1 = 0.

    Name:  Capture.PNG.jpg
Views: 40
Size:  302.8 KB

    Answer is
    2x2 - 15x + 14 = 0 ... how?
    • Thread Starter
    Offline

    18
    ReputationRep:
    Name:  Capture.PNG.jpg
Views: 22
Size:  350.5 KB
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by ckfeister)
    1. Find the quadratic equation whose roots are (α + 1) and (β + 1), where α and β are the roots of the equation 2x2 - 11x + 1 = 0.

    Answer is
    2x2 - 15x + 14 = 0 ... how?
    Rotate the picture please.

    You need to find the sum of the new roots (\alpha + 1) + (\beta + 1) = \alpha + \beta + 2 and the product of the new roots (\alpha + 1) (\beta + 1) = \alpha \beta + \alpha + \beta + 1. You should hopefully then know what to do.
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by Mr M)
    Rotate the picture please.

    You need to find the sum of the new roots (\alpha + 1) + (\beta + 1) = \alpha + \beta + 2 and the product of the new roots (\alpha + 1) (\beta + 1) = \alpha \beta + \alpha + \beta + 1. You should hopefully then know what to do.
    I don't get why its rotated like that and tried re-sending and it goes upside down... how do I rotate on TSR as phone is being useless
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by ckfeister)
    I don't get why its rotated like that and tried re-sending and it goes upside down... how do I rotate on TSR as phone is being useless
    It doesn't matter. I've stood on my head now.
    Offline

    3
    ReputationRep:
    (Original post by ckfeister)
    1. Find the quadratic equation whose roots are (α + 1) and (β + 1), where α and β are the roots of the equation 2x2 - 11x + 1 = 0.

    Name:  Capture.PNG.jpg
Views: 40
Size:  302.8 KB

    Answer is
    2x2 - 15x + 14 = 0 ... how?
    If the new roots are a+1 and b+1, then their sum is a+b+2, which is 11/2+2 = 15/2.
    Similarly their product is (a+1)(b+1) = ab+a+b+1 = 1/2+11/2+1=7.
    Hence the new equation is x^2 - (15/2)x + 7 = 0, and doubling gives 2x^2 - 15x + 14 = 0, as required.
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by HapaxOromenon3)
    ...
    Please read the Guide To Posting at the top of the Maths Forum. Providing full solutions is against the rules. You should just give hints to move people forward in their learning.
    • Thread Starter
    Offline

    18
    ReputationRep:
    Name:  Capture.PNG
Views: 23
Size:  386.0 KB

    The answer is
    x2 + 8x + 216 = 0, I get x2 - 8x + 216 = 0, anyone get why I got (+8x) instead of (-8x) ?
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    (Original post by ckfeister)

    The answer is
    x2 + 8x + 216 = 0, I get x2 - 8x + 216 = 0, anyone get why I got (+8x) instead of (-8x) ?
    The sign changes for the sum when you construct the new quadratic.

    Remember, the new quadratic is Ax^2+Bx+C=0 so the sum of roots is \alpha^3 +\beta^3=-\frac{B}{A} \Rightarrow \frac{B}{A}=-(\alpha^3 +\beta^3)
    Offline

    3
    ReputationRep:
    (Original post by Mr M)
    Please read the Guide To Posting at the top of the Maths Forum. Providing full solutions is against the rules. You should just give hints to move people forward in their learning.
    You should know by now that whenever I get banned for this or other infractions, I simply create a new account and start again. Thus you really need to try harder...
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by HapaxOromenon3)
    You should know by now that whenever I get banned for this or other infractions, I simply create a new account and start again. Thus you really need to try harder...
    This is the first time I have encountered you but I am disappointed by your reaction. No-one is threatening to ban you or sanction you in any way. I was just asking you nicely to do the right thing.
    Offline

    10
    ReputationRep:
    (Original post by hapaxoromenon3)
    you should know by now that whenever i get banned for this or other infractions, i simply create a new account and start again. Thus you really need to try harder...
    loooooooooool.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.